Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in PYTHON3):

Solution:
import math

n, h = map(int, input().strip().split())

area = (h)/(2*n)

rezi = []

alfa = math.atan(2*h)

spodnja = 1
visina = h

for _ in range(n-1):
    m = 0
    M = visina
    while abs(M-m) > 10**-10:
        sred = (M+m) / 2
        ploscina = spodnja*visina/2
        d = sred/(2*h)
        novi_a = spodnja - 2*d
        novi_visina = visina - sred
        p2 = ploscina - novi_a*novi_visina/2
        if p2 > area:
            M = sred
        else:
            m = sred
    rezi.append(sred)
    spodnja = novi_a
    visina = novi_visina

res = []

acc = 0
for e in rezi:
    acc += e
    res.append(h-acc)

res = res[::-1]
print(' '.join(map(str,res)))